WAART I

WORKSHOP IN ALGEBRAIC AND RANDOM TOPOLOGY

University of Chicago, April 18-22, 2010

Over the last few years there has been an exciting development of an area now known as "Applied Algebraic Topology", in which the powerful methods of Algebraic Topology are being applied outside of pure mathematics, and, in particular in the direction of data analysis. While it is true that at this point sophisticated applications are still rare, the gap between theory and applications is closing, and further investigation is needed to develop widely applicable, robust tools.

Independently of these developments, probabilists have developed a general theory of the topology of random fields, using primarily Integral Geometry and Differential Geometry. This theory has also found application, including in the brain imaging community, which has been using random field modelling and topological properties of these fields for quite some time, developing notions such as ``topological inference''.

The aim of this workshop, like that of its predecessor in August 2009 on the Topological Complexity of Random Sets at AIM, is to bring together algebraic topologists, probabilists, and statisticians, with the long term goal of creating an interdisciplinary, networked, community that can develop these ideas further. This is a project already supported by the National Science Science Foundation, which is funding this workshop, under a SGER grant on The Algebraic Topology of Random Fields and its Applications.

To help achieve these aims, the workshop will follow the AIM model and will be run on an informal basis, with a maximum of three formal lectures per day, focused on familiarizing participants with the background material and new developments on specific problems. Most of the schedule will include discussion and parallel working sessions.

The schedule, as it develops, is available here and a list of publications related to the workshop can be found here.

The two figures above show the persistent homology barcodes of two and three dimensional random field excursion sets. They were produced by Eliran Subag at the Technion using the PLEX: Persistent Homology Computations software of Gunnar Carlsson's Stanford group.

For additional information, please contact one of the organisers.